Sensors and Industrial Instrumentation formula sheet

Delta y_max is the largest deviation of the actual output from the reference straight line.

R_p is the total track resistance. Reduces to x for R_L infinite. The error is zero at both ends. For R_L much larger than R_p: as a fraction of the ideal reading the error is about (R_p/R_L)x(1-x), largest at x = 0.5; as a fraction of V_s (full scale) it is about (R_p/R_L)x^2(1-x), largest at x = 2/3, where it is about 0.148 R_p/R_L.

$R_p$ is the total track resistance and $R_L$ the load across the wiper. For $R_L\to \infty$ the output is $V_{s}k$, which is linear. A finite load makes it nonlinear. For $R_L\gg R_p$ the error (unloaded minus loaded output, as a fraction of $V_s$) is approximately $k^2(1-k)R_p/R_L$, largest near $k=2/3$, where it is about $0.148R_p/R_L$.

The first result is for a change of gap: sensitivity rises as the gap shrinks. The second is for a centre plate moved by $x$ from the middle of two fixed plates, each at gap $d_0$ when centred, so $C_1={\epsilon }_0{\epsilon }_{r}A/(d_0-x)$ and $C_2={\epsilon }_0{\epsilon }_{r}A/(d_0+x)$.

Gauge pressure is negative below atmospheric; absolute pressure is never negative.

SI units. p is the pressure difference between two points a vertical height h apart in a fluid of density $\rho$ at rest.

A change of 1 K equals a change of 1 °C and 1.8 °F. Use 273 when the question does.

T in °C, a and b depend on the pair. dE/dT is the thermoelectric sensitivity (Seebeck coefficient of the pair). For hot junction T_1 and cold junction T_2: E = E(T_1) - E(T_2).

Open tank, high side to the tank, low side to atmosphere; $h$ is the liquid height above the tapping point. If the transmitter sits a height $h_0$ below the tapping point (impulse line full of the same liquid), $\Delta P=\rho g(h+h_0)$, and the transmitter is given a zero suppression of $\rho g{h}_0$ so that empty still reads 4 mA.

$A$ is the displacer's uniform cross-sectional area and $h$ the submerged length (partly submerged); the buoyancy of the vapour above the liquid is neglected. Apparent weight $=W-A\rho gh$, where $W$ is the displacer's weight in air.

Linear transmitter, 4 mA at LRV and 20 mA at URV; I in mA.

Inverse of the relation above; valid for 4 mA to 20 mA.

The emitted wavelength of an LED is set by the band gap, so $E\approx E_g$. SI: $h=6.63\times 10^{-34}$ J s, $c=3\times 10^8$ m/s, $1\text{eV}=1.6\times 10^{-19}$ J.

$\Delta \lambda$ is the spectral width of the source (order-of-magnitude relation). Clear interference fringes need the path difference to be smaller than $L_c$.